Refracting Light into a Rainbow

When was the last time you saw a rainbow, anyway? Look for one. The sun has to be at your back, and there must be moisture in the atmosphere.

In the meantime, let’s go to the mathematics of refracting light to make a rainbow in this project. For our purposes, refraction is a word in physics that is used to indicate the change in the direction of a ray of light as it passes from one medium into another, assuming that its wave velocity will change also. What I mean to say is that refraction is the word we used when we talk about the change that happens to light when it goes through a medium that changes its wave velocity. For our purposes, this medium will be water. A rainbow is caused by light being refracted from air into droplets of water.

Descartes was the first person to mathematically plot this activity. As a matter of interest, this was the philosopher who made the famous quote, “I think, therefore I am.”

Scientists have established that light slows down when it goes through water.


1.Draw a graph of a right angle.

2.O is the center where the perpendicular intersects the horizontal line.

3.Dissect this angle in half, and extend the line both ways through the point where your right angle intersects O.

4.Name the angle that is closest to the perpendicular line and the dissecting line the angle A.

5.Dissect the angle underneath the horizontal line in half.

The angle that is closest to an perpendicular underneath the horizontal line will be called the B angle. The beginning of the line is point Q. The end of the line is point Z.

The line above the horizontal line represents light in air. The line beneath the horizontal line represents light in water.

Those in the know agree that the rainbow is many more colors than just the traditional seven red, orange, yellow, green, blue, indigo, and violet. We know that the rainbow is a whole continuum of colors from red to violet and even beyond the colors that the eye can see. These colors come into being because of the Law of Refraction of light through moisture. The fact that sunlight is made up of all the colors the eye can detect, and that these look white to the eye when combined was first discovered by Sir Isaac Newton in 1666.

Descartes discovered that each of the different colors of light refracted at a different degree. In addition, he discovered that there were different droplets of moisture refracting differently at the same time. To use your graph to explain this, the angle B would be different for each color. This would be multiplied exponentially. At its simplest, the basic angle is called the angle of refraction. Angle A would be called the angle of incidence.

If you want to go further, you can compute the Law of Refraction with the following equation:

The ratio of the sine of the angle of incidence to the angle of refraction is a constant.

For a practical quest, go to as many thrift stores as it takes to find an old chandelier light. Buy one crystal. Take it home. Shine a light through the prism. You’ll see many colors of the rainbow refracted onto a nearby wall. Can you explain in your own words why?